Question

Fill in the missing terms to create an equivalent expression for each polynomial

Answer 1

We have to complete the blanks with symbols and numbers so the two sides of the equality remain equal.

We can express as z the missing term (or blank).

For the first polynomial we have:

`2x+3=2x-z`

We can find the value of z as:

`\begin{gathered} 2x+3=2x-z \\ 2x-2x+3=-z \\ 3=-z \\ z=-3 \end{gathered}`

Then, we should write (-3) in the blank so that the equality becomes:

`2x+3=2x-(-3)`

For the second polynomial we have:

`7x^2+x+(-4)=7x^2+z`

In this case z will be an expression with two terms, given the blanks given. We will have to take into account the signs after we find the value of z.

Then, we can calculate z as:

`\begin{gathered} 7x^2+x+(-4)=7x^2+z \\ x+(-4)=z \\ z=x-4 \end{gathered}`

As we have to express z as a two-term expression with negative signs, we should write the equality as:

`7x^2+x+(-4)=7x^2-(-x)-4`

so the first blanck should be (-x) and the second should be 4.

Answer:

The first blank of the first expression is "-3" or "(-3)".

The first blank of the second expression is "-x" or "(-x)".

The second blank of the second expression is "4".